It's an incredible thing to see.
What happens is that the cheques have to both clear, which is the process of netting out the amounts that all financial institutions owe each other, and then settle, where the institutions pay each other the difference. When the money is going from the financial institution where you have paid your bill to the financial institution of the biller, that's the process of settling and clearing. In the meantime the money is in a suspense account and going across.
As I had said earlier in response to an earlier question, if all billers and all financial institutions were completely interconnected, the system would be fairly fragile. It would be only as strong as its weakest link. What we have right now is a very efficient and secure system.